On the DS, you could close it mid-play and pick up where you left off (Sleep Mode). You can also do this on the 3DS, but I have found that some DS games won't sleep properly when played on the 3DS (Yoshi's Island DS comes to mind).
Is there a way to make sure games enter sleep mode? I was a little disappointed to be quite a ways through a level, then I put my 3DS in sleep mode, and when I cam back 20 minutes later, the 3DS took me to the Home Screen instead of my game.
Best Answer
I don't know if this is the specific problem you're having, but there's apparently some hardware weirdness when the 3DS is in sleep mode, possibly related to sleep mode with DS games. Exposure to magnetic fields might be part of the problem. For instance, putting a 3DS on top of a DS Lite (which has magnets in the speakers in the lid) can sometimes cause this issue: